A student found the solution below for the given inequality.
1x-91<-4
x-9>4 and x-9 <-4
x> 13 and x<5
Which of the following explains whether the student is correct?
The student is completely correct because the student correctly wrote and solved the compound inequality.
The student is partially correct because only one part of the compound inequality is written correctly.
The student is partially correct because the student should have written the statements using "or" instead of "and."
The student is completely incorrect because there is no solution to this inequality.

Correct option is A) The student is completely correct because the student correctly wrote and solved the compound inequality.

Step-by-step explanation:

Here we have , A student found the solution below for the given inequality.

1x-91<-4

x-9>4 and x-9 <-4

x> 13 and x<5

We need to find Which of the following explains whether the student is correct . Let's find :

We will be solving equation 1x-91<-4  or , . We know that for Modulus function , value inside modulus function is both positive & negative depending on particular value of x ! So ,

x-9 is positive :

Let's solve

⇒  

⇒  

⇒  

x-9 is negative:

Let's solve

⇒  

⇒  

⇒  

⇒  

Therefore , Correct option is A) The student is completely correct because the student correctly wrote and solved the compound inequality.

the answer is a

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12